Forum tips

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BoldPut ** before and after the text: a**b**c —> abc

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How many binary strings of length shorter than n are there? $1+2+\ldots+2^{n-1}=2^n-1$.
How many binary strings of length exactly n? Well, $2^n$ strings. But the whole zero string was removed,
so we are left with $2^n-1$ strings. And then a one-to-one mapping exists (you, or "they", did not have to
demonstrate one explicitly in this multiple choice question).

If you're asking about a perceived ambiguity in the question, we will clarify it.
We won't answer questions along the lines of "did you mean I should answer XYZ".

Here, BTW, $n$ appearing in the question already tells you the alleged scheme is limited to a single fixed length.
(the sentence would make perfect sense without saying $n$). A similar hint comes from the answer mentioning a large enough value of $n$. A third one is saying "the all-zeros string", not "strings".